We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed technique based on prime invariants. In addition, we employ an alternative method that utilises the generators of each symmetry in the bi-adjoint representation and show how this method can be used to identify operators of any higher dimension. The accidentally symmetric 2HDMEFT potentials exhibit two classes of symmetries: (i) continuous symmetries and (ii) discrete symmetries. The number of continuous symmetries in the 2HDMEFT remains the same as in the 2HDM. However, the introduction of higher-order operators allows additional higher-order discrete symmetries, such as $Z_n$ and CP$n$. We classify the full list of the 17 accidental symmetries in the 2HDMEFT including dimension-6 and dimension-8 operators, and derive the relations that govern the theoretical parameters of the corresponding effective potentials.
We present several models where the QCD axion arises accidentally. Confining gauge theories can generate axion candidates whose properties are uniquely determined by the quantum numbers of the new fermions under the Standard Model. The Peccei-Quinn symmetry can emerge accidentally if the gauge theory is chiral. We generalise previous constructions in a unified framework. In some cases these models can be understood as the deconstruction of 5-dimensional gauge theories where the Peccei-Quinn symmetry is protected by locality but more general constructions are possible.
We discuss the problem of constructing models containing an axion and axion-like particles, motivated by astrophysical observations, with decay constants at the intermediate scale ranging from $10^9$GeV to $10^{13}$GeV. We present examples in which the axion and axion-like particles arise accidentally as pseudo Nambu-Goldstone bosons of automatic global chiral symmetries, in models having exact discrete symmetries.
The potential of $n$-Higgs Doublet Models ($n$HDMs) contains a large number of SU(2)$_L$-preserving accidental symmetries as subgroups of the symplectic group Sp(2$n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n$HDM potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). We recover the maximum…
Generic extensions of the Standard Model that respect baryon and lepton numbers have accidentally stable particles. Typical examples are the lightest exotic neutral fermion, or "neutralino", and fields with non-trivial lepton and baryon charges. In this paper we show that an accidentally stable neutralino is a natural dark matter candidate in models with warped extra dimensions. We find that annihilation into other Kaluza-Klein resonances is often allowed and very efficient. The observed dark matter abundance may then be obtained with couplings of order unity and a compactification scale above…
We consider a new approach to fermion masses and mixings in which no special "horizontal" dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries.
The extension of the Standard Model (SM) with two Higgs triplets offers an appealing way to account for both tiny Majorana neutrino masses via the type-II seesaw mechanism and the cosmological matter-antimatter asymmetry via the triplet leptogenesis. In this paper, we classify all possible accidental symmetries in the scalar potential of the two-Higgs-triplet model (2HTM). Based on the bilinear-field formalism, we show that the maximal symmetry group of the 2HTM potential is ${\rm SO(4)}$ and eight types of accidental symmetries in total can be identified. Furthermore, we examine the impact of…
The two-Higgs-triplet model (2HTM) provides us with an attractive way to simultaneously account for tiny neutrino masses and the observed matter-antimatter asymmetry in our Universe. In this talk, we study the accidental symmetries of the scalar potential in the 2HTM using the bilinear-field formalism. Based on the group-theoretical arguments, we prove that the maximal symmetry group is ${\rm SO(4)}$. We carefully analyze all the subgroups of ${\rm SO(4)}$, and find that there are eight distinct kinds of accidental symmetries in the scalar potential of the 2HTM.
Recently, it has been shown [arXiv:1106.3482] that the two-Higgs-doublet-model potential may exhibit a maximum of 13 distinct accidental symmetries. Such a classification is based on a six-dimensional bilinear scalar field formalism realizing the SO(1,5) symmetry group. This note presents the transformation relations for each of the 13 symmetries in the original scalar field space and their one-to-one correspondence to the space of scalar bilinears, thereby providing firm support for the completeness of the classification.
We reconsider the massless up quark solution of the strong CP problem. We show that an anomaly free horizontal symmetry can naturally lead to a massless up quark and to a corresponding accidental anomalous symmetry. Reviewing the controversy about the phenomenological viability of $m_u=0$ we conclude that this possiblity is still open and can solve the strong CP problem. To appear in the Proceedings of The Yukawa Couplings and the Origins of Mass Workshop.
We address two closely related problems associated with the singlet scalars' potential that are often present in supersymmetric U(1)' models, especially those which maintain the gauge unification of the MSSM in a simple way. The first is the possibility of an accidental global symmetry which results in a light Goldstone boson. The second is the problem of generating a vacuum expectation value for more than one field without reintroducing the $μ$ problem. We give sufficient conditions for addressing both issues and provide a concrete example to generate them.
Unification of matter fields implies the existence of accidental permutation symmetries, which potentially remain immune to large quantum corrections up to the TeV scale. We investigate the case of a supersymmetric $SU(5)$ grand unified theory, where such a permutation symmetry is present in the up-type squark sector. We present a variety of tests allowing to challenge the $SU(5)$ hypothesis based on the observation of squarks at the LHC. These tests appear as relations among observables involving flavour-violating or chirality-flipping decays of squarks. Moreover, they rely on top-polarimetry…
In the framework of a 3-3-1 model with a minimal scalar sector, known as the economical 3-3-1 model, we study its capabilities of generating realistic quark masses. After a detailed study of the symmetries of the model, before and after the spontaneous symmetry breaking, we find a remaining axial symmetry that prevents some quarks to gain mass at all orders in perturbation theory. Since this accidental symmetry is anomalous, we also consider briefly the possibility to generate their masses for non-perturbative effects. However, we find that non-perturbative effects are not enough to generate t…
We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an `invisible' axion arises from a single breaking of the gauge and global symmetries.
In this note, we study a large class of four-dimensional R-symmetric theories, and we describe a new quantity, τ_U, which is well-defined in these theories. Furthermore, we conjecture that this quantity is larger in the ultraviolet (UV) than in the infrared (IR), i.e. that τ_U^{UV}>τ_U^{IR}. While we do not prove this inequality in full generality, it is straightforward to show that our conjecture holds in the subset of theories that do not have accidental symmetries. In addition, we subject our inequality to an array of non-trivial tests in theories with accidental symmetries and dramatically…
We explore the possibility that lepton family numbers and baryon number are such good symmetries of Nature because they are the global remnant of a spontaneously broken gauge symmetry. An almost arbitrary linear combination of these symmetries (together with a component of global hypercharge) can be consistently gauged, if the Standard Model (SM) fermion content is augmented by three chiral SM singlet states. Within this framework of $U(1)$ extensions of the SM one generically expects flavour non-universality to emerge in the charged leptons, in such a way that naturally prevents lepton flavou…
We argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no-scale supergravities in low-energy 4D EFTs. We identify 4 nested types of no-scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no-scale properties (including non-supersymmetric flat directions). We use these ideas to classify corrections to the low-energy 4D supergravity action in perturbati…
While the $S_3$ scalar leptoquark presents a possible tree-level explanation of the $b \to s \ell \ell$ flavour anomalies, it suffers from two conceptual problems which are often disregarded by model-builders. Firstly, the quantum numbers of the $S_3$ allow for a renormalisable diquark operator that would trigger rapid proton decay unless its coupling were tuned away. Secondly, one expects the leptoquark to have generic couplings to leptons, which require tuning to avoid stringent experimental bounds on lepton flavour violation. By gauging a $U(1)$ current that acts as $L_μ- L_τ$ on the Standa…
There are four neutrino-related flavor parameters that have been measured: The three mixing angles s_{23}, s_{12}, s_{13}, and the ratio of mass-squared differences r_{23}. Of these, the first two are order one. On the other hand, s_{13} and r_{23} can be either order-one parameters that are accidentally somewhat small, or they are small for a reason, for example, they vanish in the limit of a symmetry that is broken by small parameters. We show that in the latter case, the Froggatt-Nielsen mechanism could explain the smallness of s_{13} and r_{23} only if some order-one coefficients are as sm…
We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghost-like degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbati…
We present the calculation of the short-distance power corrections to the CP-violation parameter $\varepsilon_K$ coming from dimension-8 operators in the $ΔS=2$ effective Hamiltonian. A first estimate of this contribution, obtained for large-$N_c$ and in the chiral limit, was provided in ref. [arXiv:hep-ph/0406094]. Here we evaluate and include the $\mathcal{O}(m_K^2/m_c^2)$ and $\mathcal{O}(Λ_{QCD}^2/m_c^2)$ contributions that, a priori, could induce $\mathcal{O}(1)$ corrections to previous estimates, as $m_K$ is numerically of order $Λ_{QCD}$. Our computation shows that there are several dim…
The Silence of the Dipoles: Accidental Symmetries in Lepton Flavor
Scuola Normale Superiore（高等师范学校）；INFN（意大利国家核物理研究所）；PSI Center for Neutron and Muon Sciences（PSI中子与缪子科学中心）；DAMTP, University of Cambridge（剑桥大学数学物理系）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术学院）
Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T7 and does not require extra Z_N or U(1) factors, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing wh…
We consider theories with one gauge group (SU, SO or Sp) and one scalar in a two-index representation. The renormalizable action often has accidental symmetries (such as global U(1) or unusual group parities) that lead to one or more stable states, providing Dark Matter candidates. We discuss the confined phase(s) of each theory and compute the two Higgs phases, finding no generic dualities among them. Discrete gauge symmetries can arise and accidental symmetries can be broken, possibly giving pseudo-Goldstone Dark Matter. Dark Matter candidates can have a complicated sub-structure characteris…
Tree-level accidental symmetries are known to play a fundamental role in the phenomenology of the Standard Model (SM) for electroweak interactions. So far, no significant deviations from the theory have been observed in precision, flavour and collider physics. Consequently, these global symmetries are expected to remain quite efficient in any attempt beyond the SM. Yet, they do not forbid rather unorthodox phenomena within the reach of current LHC experiments. This is illustrated with a vectophobic Two-Higgs-Doublet-Model (2HDM) where effects of a light, flavour-violating and custodian (pseudo…
